Use Mechs to capture planets, if you bombard the planet with a ship the reputation of your faction will deteriorate diminishing your popularity. If you have a second Fleet available Mechs will be a great implementation instead of having a Fleet of Battleships to Bring Control to the World. You can manage this Mech Fleet with your least skilled Admiral and have it at low capacity or with other type units like Stealth or a Megaship or whatever. Move your Attack Fleet off the World's Orbit and Move in your Mechs to Occupy it until it's under control.